Re: How long...
Personally, I'm quite happy with not being able to get a better deal than others.
It makes the process so much easier, because NOBODY has any choice, and it's not worth the faff.
That doesn't mean "we should all pay inflated prices", but "normal customers get the same deals as those who are just more diligent" isn't a bad thing.
As you hint: People don't move until there is sufficient gradient difference to overcome friction. My times costs money and saving £10 a year on electric isn't worth any amount of the most minor research and clicking buttons and tracking who I need to pay now. But when there is a differential, I invest time and effort to get a better deal.
Not having those deals means that the differential becomes zero. So we all get a decent deal. I don't spend time faffing. And electric "just costs that much". If it's too much, I'll find another utility. Same way that when phone+broadband+TV cost too much, I just bought a 4G Wifi box.
But it's a nonsense to suggest that screwing over little old grannies whose son set them up on the deal 10 years ago (and who might not be around any more!) when they don't know they could save hundreds is a good thing for any one involved. Price controls exist to protect the vulnerable like that.
Personally, I think the whole thing would be a damn sight easier if we all just paid one rate for electric from one supplier. Average it out over the country, make it so that companies make decent profit (or else they won't want to take part), everyone gets the same deal, sorted.
The time, effort and faffing saved if we did that for all such utilities would translate to everyone having more time/money.
As someone who cut £300 off my car insurance this year (literally an annual "GoCompare" so I did nothing fancy), doesn't have gas, a phone, landline broadband, a TV, etc. I assure you that I know how to save money. But for the most part it just isn't worth the time and effort, and when it is, it's for unfathomable and unrealistic reasons (e.g. my car insurance is still BISL... I just changed the company that administers on the front end with the EXACT SAME details... saved £300... there's no sense in that whatsoever... Halifax lost a customer for nearly £800, rather than lose £300, and their rival RAC picked up £500 for doing nothing but running a front-end on an existing insurer with the same details. The real irony is that the RAC included breakdown cover which I was paying for as an extra with Halifax... from the RAC...).
I wanted an electricity supplier change, but they would need to call someone out to do it because of the archaic meter. Turns out that just one day spent home waiting for them is about 3 times the cost of anything I'll save in the first year. And I might not be here in 3 year's time. And that's assuming the company I go to don't raise their prices in the future.
It's a false economy to suggest that having these companies "play off against each other" is doing anything to lower prices at all, even for the deal-seekers.
The government fixing the prices kills the commercial market overnight and customers pay what they would have paid anyway, without the faffing and advertising and paperwork and admin and duplication of effort that all those companies are doing to "win" customers, not to mention shareholder deals etc. It also means we can all just get on with our lives and not have to waste time changing suppliers and checking prices in the first place. Hell, it would kill all the price comparison sites overnight too. What's to compare?
I think it's just a placebo, "getting the best prices". If you fail to do it, sure you will lose out. But doing it doesn't mean you'll get something any better than what you'd get with just blanket regulation and fixed prices. Just the sheer removal of so many private-owned, shareholder-paying, corporate middle-men should remove enough to get you a better price that ever. The trick is to "nationalise" without letting government cronies get their 10% either. You can only do that with transparency and calling them out, and yet no-one cares that most ministers are profiting from exactly the industries they are supposed to be regulating because there's a bit of paper somewhere that says that.